<PAGE>   1


                     U.S. SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

                                   FORM 10-QSB

(Mark One)

 X       QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(D) OF THE
---      SECURITIES EXCHANGE ACT OF 1934
         For the quarterly period ended:  September 30, 1997

         TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(D) OF THE SECURITIES
---      EXCHANGE ACT OF 1934 
         For the transition period from _______________ to ________________

                        Commission file number: 33-43317

                              EASTON BANCORP, INC.
        -----------------------------------------------------------------
        (Exact name of small business issuer as specified in its charter)

       Maryland                                         52-1745344
------------------------                    ------------------------------------
(State of incorporation)                    (I.R.S. Employer Identification No.)

                   501 Idlewild Avenue, Easton, Maryland 21601
                   -------------------------------------------
                    (Address of principal executive offices)

                                 (410) 819-0300
                           ---------------------------
                           (Issuer's telephone number)

                                 Not Applicable
              ----------------------------------------------------
              (Former name, former address and former fiscal year,
                          if changed since last report)


         Check whether the issuer: (1) filed all reports required to be filed by
Section 13 or 15(d) of the Exchange Act during the past 12 months (or for such
shorter period that the registrant was required to file such reports), and (2)
has been subject to such filing requirements for the past 90 days. Yes X No
                                                                      --   --

         State the number of shares outstanding of each of the issuer's classes
of common equity, as of the latest practicable date:

         On November 7, 1997, 559,328 shares of the issuer's common stock, par
value $.10 per share, were issued and outstanding.

         Transitional Small Business Disclosure Format (check one): Yes   No X
                                                                       --    --


<PAGE>   2



                                     PART I
                              FINANCIAL INFORMATION

ITEM 1.  FINANCIAL STATEMENTS.

                       EASTON BANCORP, INC. AND SUBSIDIARY
                           CONSOLIDATED BALANCE SHEETS
                                   (Unaudited)

<TABLE>
<CAPTION>
                                                       September 30,      December 31,
                                                            1997              1996
                                                            ----              ----
<S>                                                    <C>                <C>        
                    ASSETS
Cash and due from banks                                 $ 1,306,970       $ 1,211,182
Federal funds sold                                        3,058,726         2,824,727
Investment in Federal Home Loan Bank stock                  124,500           121,600
Investment securities held-to-maturity (market
  value of $1,501,528 and $1,247,275, respectively)       1,500,000         1,250,000
Loans, less allowance for credit losses of
  $358,000 and $332,253, respectively                    32,902,091        30,062,431
Premises and equipment, net                               1,715,085         1,515,354
Intangible assets, net                                       35,223            84,503
Accrued interest receivable                                 229,572           181,009
Other assets                                                 83,085            44,134
                                                        -----------       -----------
    Total assets                                        $40,955,252       $37,294,940
                                                        ===========       ===========

           LIABILITIES AND STOCKHOLDERS' EQUITY
Deposits
  Noninterest-bearing                                   $ 2,427,133       $ 1,719,187
  Interest-bearing                                       34,026,907        31,039,372
                                                        -----------       -----------
    Total deposits                                       36,454,040        32,758,559
Accrued interest payable                                     93,086            93,684
Securities sold under agreements to repurchase              443,762           574,328
Other liabilities                                            41,127           145,578
                                                        -----------       -----------
    Total liabilities                                    37,032,015        33,572,149
                                                        -----------       -----------

Stockholders' equity
  Common stock, par value $.10 per share;
    authorized 5,000,000 shares, 559,328
    shares issued and outstanding                            55,933            55,933
  Additional paid-in-capital                              5,217,686         5,217,686
  Retained earnings (deficit)                            (1,350,382)       (1,550,828)
                                                        -----------       -----------
    Total stockholders' equity                            3,923,237         3,722,791
                                                        -----------       -----------
    Total liabilities and stockholders' equity          $40,955,252       $37,294,940
                                                        ===========       ===========
</TABLE>


See accompanying Notes to Consolidated Financial Statements.


                                        1

<PAGE>   3



                       EASTON BANCORP, INC. AND SUBSIDIARY
                        CONSOLIDATED STATEMENTS OF INCOME
                                   (Unaudited)

<TABLE>
<CAPTION>
                                             Three Months Ended           Nine Months Ended
                                                September 30,               September 30,
                                            ---------------------     -------------------------
                                              1997         1996          1997           1996
                                            --------     --------     ----------     ----------
<S>                                         <C>          <C>          <C>            <C>       
Interest revenue
  Loans, including fees                     $751,863     $594,331     $2,160,573     $1,721,181
  Investment securities                       22,330       10,269         62,187         26,281
  Federal funds sold                          56,561       90,153        162,974        298,225
                                            --------     --------     ----------     ----------
    Total interest revenue                   830,754      694,753      2,385,734      2,045,687

Interest expense                             417,765      367,737      1,198,575      1,120,077
                                            --------     --------     ----------     ----------

    Net interest income                      412,989      327,016      1,187,159        925,610

Provision for loan losses                      8,285        9,066         49,751         34,162
                                            --------     --------     ----------     ----------

    Net interest income after
      provision for loan losses              404,704      317,950      1,137,408        891,448
                                            --------     --------     ----------     ----------

Other operating revenue                       21,382       37,155         70,898         93,132
                                            --------     --------     ----------     ----------

Other expenses
  Salaries and benefits                      190,767      162,426        540,170        474,438
  Occupancy                                   20,352       21,134         58,079         62,423
  Furniture and equipment                     26,742       24,548         74,746         69,671
  Other operating                            114,902       85,693        334,865        262,520
                                            --------     --------     ----------     ----------
    Total operating expenses                 352,763      293,801      1,007,860        869,052
                                            --------     --------     ----------     ----------

Net income before income taxes                73,323       61,304        200,446        115,528

Income taxes                                    --           --             --             --
                                            --------     --------     ----------     ----------

Net income                                  $ 73,323     $ 61,304     $  200,446     $  115,528
                                            ========     ========     ==========     ==========

Earnings per common share                   $    .12     $    .10     $      .33     $      .19
                                            ========     ========     ==========     ==========

Earnings per common share fully diluted     $    .12     $    .10     $      .33     $      .19
                                            ========     ========     ==========     ==========
</TABLE>


See accompanying Notes to Consolidated Financial Statements.


                                        2

<PAGE>   4



                       EASTON BANCORP, INC. AND SUBSIDIARY
                      CONSOLIDATED STATEMENTS OF CASH FLOWS
                                   (Unaudited)


<TABLE>
<CAPTION>
                                                                      Nine Months Ended
                                                                         September 30,
                                                                 ----------------------------
                                                                     1997            1996
                                                                 -----------      -----------
<S>                                                              <C>              <C>        
CASH FLOWS FROM OPERATING ACTIVITIES
  Interest received                                              $ 2,337,074      $ 2,021,174
  Other revenue received                                              62,836           86,467
  Cash paid for operating expenses                                (1,019,103)        (770,020)
  Interest paid                                                   (1,199,173)      (1,126,072)
                                                                 -----------      -----------
                                                                     181,634          211,549
                                                                 -----------      -----------
CASH FLOWS FROM INVESTING ACTIVITIES
  Cash paid for premises, equipment and software                    (274,548)          (6,692)
  Net loans to customers                                          (3,249,080)      (2,374,557)
  Loan participations purchased                                         --           (344,346)
  Loan participations sold                                           359,766             --
  Purchase of investment securities                               (1,252,900)        (250,000)
  Proceeds from sales/maturities of investments                    1,000,000             --
  Proceeds from sale of other real estate owned                         --            113,804
                                                                 -----------      -----------
                                                                  (3,416,762)      (2,861,791)
                                                                 -----------      -----------
CASH FLOWS FROM FINANCING ACTIVITIES
  Net increase in deposits                                         3,695,481        2,865,976
  Net increase (decrease) in securities sold under
     agreements to repurchase                                       (130,566)         (25,281)
                                                                 -----------      -----------
                                                                   3,564,915        2,840,695
                                                                 -----------      -----------

NET INCREASE IN CASH AND CASH EQUIVALENTS                            329,787          190,453
CASH AND CASH EQUIVALENTS AT BEGINNING OF PERIOD                   4,035,909        5,491,301
                                                                 -----------      -----------

CASH AND CASH EQUIVALENTS AT END OF PERIOD                       $ 4,365,696      $ 5,681,754
                                                                 ===========      ===========

RECONCILIATION OF NET INCOME TO NET CASH
   PROVIDED BY OPERATING ACTIVITIES
  Net income                                                     $   200,446      $   115,528
  Adjustments to reconcile net income to net cash
    provided by operating activities:
       Depreciation and amortization                                 124,097          114,870
       Provision for loan losses                                      49,751           34,162
       Increase in accrued interest receivable and
          other assets                                               (87,514)         (41,495)
       Increase (decrease) in operating accounts payable and
          other liabilities                                         (105,049)          (3,758)
       Deferred loan origination fees                                    (97)          (3,697)
       Gain on sale of other real estate                                --             (4,061)
                                                                 -----------      -----------
                                                                 $   181,634      $   211,549
                                                                 ===========      ===========
Noncash activity:
  Other real estate acquired through foreclosure                 $      --        $   109,743
                                                                 ===========      ===========
</TABLE>


See accompanying Notes to Consolidated Financial Statements.

                                        3

<PAGE>   5



NOTES TO CONSOLIDATED FINANCIAL STATEMENTS:

1.       Basis of Presentation

         The accompanying unaudited condensed financial statements have been
prepared in accordance with generally accepted accounting principles for interim
financial information and with the instructions to Form 10-QSB and Item 310(b)
of Regulation S-B of the Securities and Exchange Commission. Accordingly, they
do not include all the information and footnotes required by generally accepted
accounting principles for complete financial statements. In the opinion of
management, all adjustments (consisting of normal recurring accruals) considered
necessary for a fair presentation have been included. Operating results for the
nine months ended September 30, 1997, are not necessarily indicative of the
results that may be expected for the year ended December 31, 1997. For further
information, refer to the consolidated financial statements and footnotes
thereto for the Company's fiscal year ended December 31, 1996, included in the
Company's Form 10-KSB for the year ended December 31, 1996.

2.       Cash Flows

         For purposes of reporting cash flows, cash and cash equivalents include
cash on hand, unrestricted amounts due from banks, overnight investments in
repurchase agreements, and federal funds sold.

3.       Adoption of New Accounting Principles

         During the first quarter of 1997, the Company adopted Financial
Accounting Standards Board Statement No. 125 "Accounting for Transfers and
Servicing of Financial Assets and Extinguishments of Liabilities." Under this
principle, financial assets are recognized based on the assets the Company
controls and are removed from the balance sheet when control is surrendered.
Liabilities are recorded when incurred.


                                        4

<PAGE>   6



ITEM 2.  MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND
RESULTS OF OPERATIONS.

         Easton Bancorp, Inc. (the "Company") was incorporated in Maryland on
July 19, 1991, primarily to own and control all of the capital stock of Easton
Bank & Trust Company (the "Bank") upon its formation. The Bank commenced
business on July 1, 1993, and the only activity of the Company since then has
been the ownership and operation of the Bank. The Bank conducts a general
commercial banking business in its service area, emphasizing the banking needs
of individuals and small- to medium-sized businesses and professional concerns.

         The following discussion of the financial condition and results of
operations of the Company should be read in conjunction with the Company's
unaudited financial statements and related notes and other statistical
information included elsewhere herein.

Results of Operations

         Net income for the Company for the three months ended September 30,
1997, was $73,323, compared to $61,304 during the corresponding period of 1996.
Net income for the nine months ended September 30, 1997, was $200,446, compared
to $115,528 for the corresponding period of 1996. The increase in net income can
be attributed primarily to the increase in net interest income. The increase in
net interest income is primarily the result of the increase in the Bank's loan
portfolio from $26,816,470 at September 30, 1996, to $32,902,091 at September
30, 1997.

         The Bank's provision for loan losses was $8,285 for the quarter ended
September 30, 1997, and $49,751 for the nine months ended September 30, 1997,
compared to $9,066 for the quarter ended September 30, 1996, and $34,162 for the
nine months ended September 30, 1996. The allowance for loan losses was $358,000
at September 30, 1997, or 1.08% of total loans, compared to $332,253 at December
31, 1996, or 1.09% of total loans. Management believes that the allowance for
loan losses reflects an amount that is more than adequate to cover future losses
in the loan portfolio; however, there can be no assurance that loan losses in
future periods will not exceed the allowance for loan losses or that additional
increases in the allowance will not be required.

         Noninterest expense increased $58,962, or 20.1%, to $352,763 for the
quarter ended September 30, 1997, from $293,801 for the quarter ended September
30, 1996. The increase was primarily related to the increase in other operating
expenses of $29,209, and increases in salaries and benefits of $28,341. The
increase in other operating expenses for the three months ended September 30,
1997, compared to the same period for 1996, was primarily due to increased
expenses in printing and supplies of $9,369, advertising of $3,159, data
processing of $3,563 and entertainment of $2,458. Also, effective April 1997 all
directors are paid $25 for each committee meeting they attend. This accounted
for an increase in director fees of $2,800 for the quarter ended September 30,
1997, compared to the same period of 1996. The increase in salaries and benefits
was due to annual salary increases, the accrual of bonuses for employees and
officers, and two new employees hired in June 1997 and one part-time employee
hired in July 1997.

         Return on average assets and average equity, on an annualized basis,
for the quarter ended September 30, 1997, were .75% and 7.24%, respectively,
compared to .69% and 6.82%, respectively, for the same quarter of 1996. Return
on average assets and average equity, on an annualized basis, for the nine
months ended September 30, 1997, were .68% and 7.00%, respectively, compared to
 .45% and 4.34%, respectively, for the same period of 1996. Earnings per share on
a fully diluted basis for the


                                        5

<PAGE>   7



quarter and nine months ended September 30, 1997, were $.12 and $.33,
respectively, compared to $.10 and $.19, respectively, for the same periods of
1996.

         The Company's assets ended the third quarter of 1997 at $41.0 million,
an increase of $3.7 million, or 9.8%, from $37.3 million at December 31, 1996.
This increase is primarily the result of the $2.8 million increase in loans, the
$233,999 increase in federal funds sold, and the $250,000 increase in investment
securities held-to-maturity. The increase in loans is a result of the
development and growth of the Bank and the related growth in deposits. Total
deposits ended the quarter at $36.5 million, an increase of $3.7 million, or
11.3%, from $32.8 million at December 31, 1996. At September 30, 1997, the
Company's loan to deposit ratio was 90.3%, compared to 91.8% at December 31,
1996.

         Management expects that its 1997 income will exceed expenses. The net
income of $73,323 for the quarter ended September 30, 1997, is the largest
profit shown for any quarter since the Bank opened in July 1993. The growth of
loans and deposits and the associated increase in net interest income are the
primary reasons for the increased income. Although management expects that the
Company's current profitably will continue, future events, such as an
unanticipated deterioration in the loan portfolio, could reverse this trend.
Management's expectations are based on management's best judgement and actual
results will depend on a number of factors that cannot be predicted with
certainty and thus fulfillment of management's expectations cannot be assured.

Liquidity and Sources of Capital

         The $3.7 million increase in deposits from December 31, 1996, to
September 30, 1997, is primarily reflected in the $2.8 million increase in
loans, the $233,999 increase in federal funds sold and the $250,000 increase in
investment securities held-to-maturity. The Company's primary source of
liquidity is cash on hand plus short-term investments. At September 30, 1997,
the Company's liquid assets totaled $5,990,196, or 14.6% of total assets,
compared to $5,407,509, or 14.5% of total assets, at December 31, 1996. The
Company has a $3,500,000 secured line of credit with the Federal Home Loan Bank
of Atlanta, a $1,000,000 line of credit, secured by investment securities of the
Bank, from a correspondent bank, and a $1,000,000 unsecured line of credit from
another correspondent bank, all for future liquidity. If additional liquidity is
needed, the Bank will sell participations in its loans.

         The capital of the Company and the Bank exceeded all prescribed
regulatory capital guidelines at September 30, 1997. At September 30, 1997, the
Tier 1 leverage ratio for the Bank was 9.63%. At September 30, 1997, the Bank
had a risk-weighted total capital ratio of 13.59%, and a Tier 1 risk-weighted
capital ratio of 12.43%. The Company expects that its current capital and
short-term investments will satisfy the Company's cash requirements for the
foreseeable future. However, no assurance can be given in this regard as rapid
growth, deterioration in the loan quality or poor earnings, or a combination of
these factors, could change the Company's capital position in a relatively short
period of time.


                                     PART II
                                OTHER INFORMATION

ITEM 1.  LEGAL PROCEEDINGS.

         There are no material pending legal proceedings to which the Company or
the Bank is a party or of which any of their property is the subject.


                                        6

<PAGE>   8




ITEM 2.  CHANGES IN SECURITIES.

         Not applicable.

ITEM 3.  DEFAULTS UPON SENIOR SECURITIES.

         Not applicable.

ITEM 4.  SUBMISSION OF MATTERS TO A VOTE OF SECURITY HOLDERS.

         There were no matters submitted to a vote of security holders during
the quarter ended September 30, 1997.

ITEM 5.  OTHER INFORMATION.

         None.

ITEM 6.  EXHIBITS AND REPORTS ON FORM 8-K.

         (a)      Exhibits.

                  3.1      Articles of Incorporation of the Company
                           (incorporated by reference to Exhibit 3.1 of
                           Registration Statement on Form S-18, File No.
                           33-43317).

                  3.2      Bylaws of the Company (incorporated by reference to
                           Exhibit 3.2 of Registration Statement on Form S-18,
                           File No. 33-43317).

                  10.1     Employment Agreement dated July 22, 1991, between the
                           Company and Thomas P. McDavid (incorporated by
                           reference to Exhibit 10.1 of Registration Statement
                           on Form S-18, File No. 33-43317).

                  10.2     Easton Bancorp, Inc. 1991 Stock Option Plan
                           (incorporated by reference to Exhibit 10.2 of
                           Registration Statement on Form S-18, File No.
                           33-43317).

                  10.3     Form of Warrant Agreement (incorporated by reference
                           to Exhibit 10.3 of Registration Statement on Form
                           S-18, File No. 33-43317).

                  11       Computation of Earnings Per Share.

                  27       Financial Data Schedule (for SEC use only).

         (b)      Reports on Form 8-K.

                  There were no reports on Form 8-K filed by the Company during
                  the quarter ended September 30, 1997.

                                        7

<PAGE>   9



                                   SIGNATURES


         In accordance with the requirements of the Exchange Act, the registrant
caused this report to be signed on its behalf by the undersigned, thereunto duly
authorized.

                                    EASTON BANCORP, INC.
                                    --------------------------------------
                                    (Registrant)



Date:    November 11, 1997          By:  /s/ Thomas P. McDavid
       --------------------             ----------------------------------
                                             Thomas P. McDavid
                                             President



Date:    November 11, 1997          By:  /s/ Pamela A. Mussenden
       --------------------             ----------------------------------
                                             Pamela A. Mussenden
                                             Assistant Treasurer
                                             (Principal Financial Officer)


                                        8

<PAGE>   10




                                INDEX TO EXHIBITS

<TABLE>
<CAPTION>
Exhibit                                                                                 Sequential
Number                              Description                                         Page Number
------                              -----------                                         -----------
<S>      <C>                                                                            <C>    
3.1      Articles of Incorporation of the Company (incorporated by reference to
         Exhibit 3.1 of Registration Statement on Form S-18, File No. 33-43317).

3.2      Bylaws of the Company (incorporated by reference to Exhibit 3.2 of
         Registration Statement on Form S-18, File No. 33-43317).

10.1     Employment Agreement dated July 22, 1991, between the Company and
         Thomas P. McDavid (incorporated by reference to Exhibit 10.1 of
         Registration Statement on Form S-18, File No. 33-43317).

10.2     Easton Bancorp, Inc. 1991 Stock Option Plan (incorporated by reference
         to Exhibit 10.2 of Registration Statement on Form S-18, File No. 33-
         43317).

10.3     Form of Warrant Agreement (incorporated by reference to Exhibit 10.3 of
         Registration Statement on Form S-18, File No. 33-43317).

11       Computation of Earnings Per Share.

27       Financial Data Schedule (for SEC use only).
</TABLE>